"What is your home task?"
Translation:Яке твоє домашнє завдання?
Yes, this also sounds natural.
[Although I'd use «в» and not «у» here, because «яке» ends in a vowel, but у/в alteration is not taught in this course...]
I didn't realize the у/в alteration was applicable to genitive possessive as well as to locutive/prepositional.
Yes, and in a conversation about homework such a loose translation is preferable. It means exactly "What do you need to do" and not something else like is it interesting/difficult etc.